Efficient inversion of doubly block Toeplitz matrix

An iterative algorithm for the inversion of a doubly block Toeplitz matrix consisting of m × m blocks of size p × p is described. The algorithm presented exploits the structure of the doubly block Toeplitz matrix and outperforms Akaike's algorithm by a factor of \max {2 \frac{p}{m},2} . The use of this algorithm for an iterative solution of a doubly block Toeplitz set of linear equations is also presented.